Nouveau driver uses MESA opengl software rasterizer, so there can no libGLcore.so.1 at all.

The trouble applies to all old video cards owners (chips like NV34, etc.) - there is no support for native video drivers since it uses version 11 of XFree ABI video driver, which is incompatible with 173.14.xx native nvidia drivers...

the reason is that old adapter is not supported anymore by nvidia proprietary drivers for XFree ABI video driver of v.11, which is in its turn used in Ubuntu 12.04, when the proprietary nvidia drivers are compiled for XFree ABI video driver of v.10, which is in its turn used in Ubuntu 11.10. As far as I know NVidia doesn't want to recompile its drivers for XFree ABI video driver of v.11.

But the trouble could be worked around if VirtualBox is set not to require OpenGL by default, only if checkboxes of 2D&3D Acceleration are checked. For e.g., who does need 2D&3D accel. for FreeBSD or any other textual guest boxes? There is no need in OpenGL...

I still don't understand the problem. If you were able to install the VirtualBox package then all required libraries should be installed including the GL library, otherwise some package is broken.

Why? There's no check for OpenGL hardware/driver support during installation. Such capabilities are checked when VirtualBox starts.

I did notice no problem installing due to absence of hardware/driver OpenGL support in Nouveau -driver enviroment.

There is no problem to install.

There is problem to launch in nouveau-driver env.:
VirtualBox: supR3HardenedMainGetTrustedMain: dlopen("/usr/lib/virtualbox/VirtualBox.so",) failed: libGLcore.so.1: cannot open shared object file: No such file or directory

Nouveau is not native driver, but the only supporting my NV34 in Ubuntu 12.04. libGLcore.so.1 comes with native drivers only. Nowadays there is no (and is not planned) native nvidia driver for Ubuntu 12.04 and X.Org xserver 1.10 it uses by default.

The trouble could be worked around if VirtualBox is set not to require OpenGL by default, only if checkboxes of 2D&3D Acceleration are checked. For e.g., who does need 2D&3D accel. for FreeBSD or any other textual guest boxes? There is no need in OpenGL...

Let me explain this again. VirtualBox depends on the OpenGL libraries, that is true. But the VirtualBox package has package dependencies to packages providing the libraries the VirtualBox binaries is linked against. This is the Debian package management and if you installed all packages without any tweaks then the required libraries are installed, regardless which package provides the libraries and there is no workaround required. In case of Precise the package dependency is libgl1-mesa-glx | libgl1 and after installing any package which satisfies this dependency, VirtualBox should start.